If Z−2Z−6i  is purely real then the locus of Z  is ( where z=x+iy)

(x−2)+iyx+i(y−6)  is purely real I.P = 0 ⇒  xy – (x – 2) (y – 6) = 0           ⇒  xy – [xy – 6x – 2y + 12] = 0        ⇒ 6x + 2y – 12 = 0  ⇒  3x + y – 6= 0